Print and play!

Let's have a look at the first puzzle of the book One Way, in the Alcazar app (available for iOS and Android).

With a bit of experience in puzzle solving, you will probably start this one by filling the squares that have two walls (cornersandpipes), and end up with all the black lines on the image.

Experts will go one step further and trace all the red lines on this image. With some practice, this step will become trivial, and you will do it automatically.

But what is it about? It's a simple technique that I call Bouncing. I'll show you how to use it in the 4x2 upper-right room of this puzzle.

The basic idea of bouncing is the same as the Weak Points technique
that I presented a few months ago, when Alcazar was still a paper-only puzzle. Start by completing square #1 (it's a corner), and move to square #2. Notice that there are only two possible ways
to cross that square: left-up (A), or left-right (B). In conclusion, you must enter this square from the left.

Now you can start bouncing. Very often, when you draw a conclusion from a weak point like this, you create another weak point in a nearby square. You can bounce from square to square
and draw many conclusions for the price of one.

In our example, let's bounce to square #3. Because of the line that we traced in square #2, it's now impossible to cross square #3 down-right: this would
automatically create a 6-squares cycle. Thus, there are only 2 possible ways to cross square #3: left-down (A) and left-right (B). In conclusion: you must
enter this square from the left.

Let's continue bouncing! There are 2 ways to cross square #4: right-down (A) or up-down (B). Conclusion: you must enter from the bottom.

This technique can be used in the vast majority of Alcazar puzzles. If you play often, this will be automatic for you. You will bounce from square to square without thinking about it.

The key idea is to notice that all the possible lines fall into two categories: those that fill an even number of squares, and those that fill an odd number of squares. When the puzzle is
colored like a checkerboard (black, white, black, white...), you can extract important information about these lines (see image).

Solution to the first puzzle

With 18 white squares and 17 black ones, we need an odd path to fill this room, and it needs to start and end on a white square. Unfortunately, there is only one
door on a white square. This is why the puzzle has no solution.

Solution to the second puzzle

It was meant to be much harder than the first one, but "jh" (one of the blog's reader) came up with a very elegant solution that I summarize here. Congratulations, jh!

Like the first puzzle, this one has an extra white square, which means that the solution must start and end on a white square. We can close all the black exits of the
puzzle.

Then, let's have a look at the 6x6 area in the bottom right. It has as many white squares as black ones, which means that if we want to fill this area with a single line, this line will
need to start on a white square and end on a black one (or vice versa). But now that the puzzle's black exits are closed, this area has only white exits. In conclusion: we cannot fill
it with a single line.

One last question remains: could we fill this area with more than one than one line? In other words, could we enter this area, exit, and then enter it again? Let's see...

There are only 3 squares that link this area to the rest of the puzzle and they are white. It means that we must enter and exit on white squares with our first path, and then, enter again on
a white square before exiting the whole puzzle (again, on a white square). Each of our lines will cross one extra white square, but the area doesn't have extra white squares.

And that's why the puzzle has no solution.

What about normal puzzles?

Click to play in your browser

When playing some of the advanced puzzles in the real game, using the square colors can be very useful. Look at the first level of the book "The Six Rooms", for example. The upper right
room has an even number of squares and 4 exits: 3 are white and one is black. Conclusion: you must use the black one.

I hope that this article was helpful. Don't forget to get the Alcazar app (iOS and Android), and if you like it, leave a comment and a rating!

Small Alcazars can be solved with just a bit of intuition, but as you tackle larger levels, the many elegant and complex techniques of the game become more and more relevant.

It's much more fun to find these techniques by yourself than to read about them, so let me simply propose an exercise that may put you on the right path. Here are two Alcazar
puzzles. I made the first one, and the second one was created by Edderiofer. Don't try to solve them! They are both impossible. But why? How can you prove that they have no solution?

Leave your questions and hints in the comments! You may use ROT13 (http://www.rot13.com/) to hide important clues for those who don't want to see them. I will give a complete explanation in
about a week. Have fun!

Thanks to everyone who asked to join the group of testers! I apologize for making you wait, but I have good news: next weekend, the app will enter a short beta test phase, and I will accept
everyone who asked, as testers.

It also means that the Android app will soon be available for everyone!

If you didn't do it already, you can join the beta test by asking to be part of this group on Google+: